college

Students still need to learn principles

Joy Buchanan1 Comment

Sometimes I get weeks in the summer that are more research focused. This past week is very much a teaching and service focused week at my university. I haven’t had any time to ponder topics related to research or current events. So, I will share what I’ve been telling my fellow college educators. This will sound backward to some and like common sense to others. Feel free to comment with your thoughts.

College professors who teach 200-level or “principles” classes should not change all that much in response to AI. Students still need to know something. There need to be a few concepts and vocabulary words in their heads. For example, a person cannot use a calculator effectively if they do not know what a square root is at all.

I see highly trained mid-career professionals bragging about how they get ChatGPT to do their work. Can a 20-year-old do that if they don’t know what words to use in a prompt? How does vibe coding go for people who never learned to write out a single line of code? (not a question I have an expert answer to right now)

We should largely be sticking to the “old ways” and at least to some extent still require memorization. Having an exam on paper is a good way to ensure that the students can form coherent thoughts of their own, when possible.

Indeed, students might become AI jockeys when they get to the workplace. A 400-level class would be a good place for them to start heavily integrating AI tools to accomplish tasks and do projects. For anyone unfamiliar with American college categories, that would mean that an undergraduate might heavily use AI tools in their 4th and final year of study.

AI makes a great tutor for learning and enforcing principles, but it should not serve as a replacement test-taker. A human who cannot read and write will not be able to take full advantage of an intelligent machine in the next decade. Voice recognition is getting very good and the models are getting more agentic, so this might all change if we can keep the data centers on long enough. In the future, you might argue that having students write an exam answer by hand is as superfluous as teaching them to play the violin.

As of 2025, what you might see is some teachers who feel pressured to claim they are integrating AI more than they actually want to. A relative I talked to his summer in a corporate job told me that she feels intense pressure at work to be able to claim that she’s using AI. Anyone doesn’t have the appearance of embracing AI looks behind or expendable!

Probability Theory for the Minecraft Generation

Joy Buchanan1 Comment

If you are teaching statistics to 20-year-olds (or maybe even if you are not), you might be interested in ways to make probability theory more engaging. I watched a students eyes light up when I showed this in class, so that makes it feel worth sharing.

The Law of Large Numbers is a standard part of statistics or business analytics classes. Something that goes along with it conceptually is “The Law of Truly Large Numbers,” sometimes also called The Infinite Monkey Theorem. The idea is that if you put monkeys in front of typewriters, perhaps infinite monkeys with infinite typewriters and with infinite time, they will eventually write a Shakespeare play.

To illustrate this feature of probability theory for the video gamers, a fun and well-produced video is
“Can Mobs Beat Minecraft?” by Wifies

There is nothing inappropriate for students. The video is 13 minutes, which is too long to show during a class session. I recommend watching the first minute and a half and then explaining that the middle is a lot of gaming details to prove that it is technically possible that a randomly acting “mob” could eventually beat the entire Minecraft game, given enough time.

At the 10-minute mark, the math begins. You could watch about one more minute and a half to see how he tries to calculate the infinitesimally-small-and-yet-positive probability that this could happen. Given enough time, just about anything that is possible will happen.

Another possibility for a teacher is not to show the video in class but to offer it as an optional or extra credit assignment, so that a student who loves Minecraft could really have fun with it and other students can skip.

For me, this pairs with Chapter 5 on Probability for the textbook Applied Statistics in Business and Economics.

Another teaching tip. If you ever need to print out paper rulers, you might be Googling “printable rulers” and you’ll see a bunch of scams as the top results. THIS link works: https://www.brightonk12.com/cms/lib/MI02209968/Centricity/Domain/517/Ruler_6-inch_by_16.pdf

Selectivity and Selection Bias: Are Selective Colleges Better?

Jeremy Horpedahl1 Comment

If you have ever been through the process of applying to colleges, you have almost certainly heard the term “selective colleges.” If you haven’t the basic idea is that some colleges are harder to get into, for example as measured by what percentage of applicants are accepted to the school. The assumption of both applicants and schools is that a more selective college is “better” in some sense than a less selective college. But is it?

In a new working paper, Mountjoy and Hickman explore this question in great detail. The short version of their answer: selective colleges don’t seem to matter much, as measured by either completion rates or earnings in the labor market. That’s an interesting result in itself, but understanding how they get to this result is also interesting and an excellent example of how to do social science correctly.

Here’s the problem: when you just look at outcomes such as graduation rates or earnings, selective colleges seem to do better. But most college freshmen could immediately identify the problem with this result: that’s correlation, not causation (and importantly, they probably knew this before stepping onto a college campus). Students that go to more selective colleges have higher abilities, whether as measured by SAT scores or by other traits such as perseverance. It’s a classic selection bias problem. How much value is the college really adding?

Here’s how this paper addresses the problem: by only looking at students that apply to and are accepted to colleges with different selectivity levels, but some choose to go to the less selective colleges. What if we only compare this students (and of course, control for measurable differences in ability)?

Now this approach is not a perfect experiment. Students are not randomly assigned to different colleges. There is still some choice going on. But are the students who choose to attend a less selective college different in some way? The authors try to convince us in a number of ways that they are not really that different. Here’s one thing they point out: “nearly half of the students in our identifying sample choose a less selective college than their most selective option, suggesting this identifying variation is not merely an odd choice confined to a small faction of quirky students.”

Perhaps that alone doesn’t convince you, but let’s proceed for now to the results. This chart on post-college earnings nicely summarizes the results (see Figure 3 in the paper, which also has a very similar chart for completion rates)

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Back to School! But what’s up with college pricing?

Jeremy Horpedahl1 Comment

It’s time to head back to school! Which means it’s time for college students to once again ask the question: How am I going to pay for this?

It’s common knowledge that college is expensive and getting more expensive every year. A Google search for “skyrocketing tuition” produces almost 60,000 results. But whenever a fact is so commonly accepted, it’s worth asking if it’s really true.

Here’s one way to think about: are college tuition and fees increasing faster than the overall rate of inflation? For much of recent history, the answer has been most definitely “yes.” I start the series here in 2006, because there were some methodological changes to the index just before 2006. Cumulatively, college tuition and fees (as measured in the CPI) have increased by 78%, while prices overall have only increased by about 38%.

But for the very recent history, since 2017, the answer is “no.” College tuition and fees have often been increasing at slower rates than overall prices in the CPI, and the difference is especially dramatic in 2021. Since 2017, overall prices have increased by about 12.4%, but college tuition and fees has only increased by 7.8%.

However, even this data overstates how much tuition and fees have gone up for undergraduates in the US!

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